Q$24.$ An air conditioning system is to be installed in an engine room. Information from a manufacturer's catalogue indicates that, at a flow rate of $\backslash (4\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash ),$ the loss of total pressure across the AHU alone will be $144$ Pa $.$ Design calculations reveal that, at a flow rate of $\backslash (5\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash ),$ the loss of total pressure across the supply duct will be $80$ Pa $.$ The fan, whose characteristic is given in the table below, is to be installed downstream of the AHU. Answer the following:

a$.$ Plot the system characteristic curve and the fan curve.

b$.$ Determine the operating flow rate and the total pressure just downstream of the fan.

$[4\mathrm{.}8$ m$3/$s$,93$ Pa$\backslash (]\backslash )$